[Googolplex]

I've found that disrupting the Airplay connection long enough will cause it to work correctly for at least awhile when it reconnects. The easiest way to do this is to turn off wifi on the iOS device until your Airplay option disappears and then turn it back on again. You might have to do this a few times for it to work. The tiny bit of good news in this is that it is at least easier to get to the wifi setting and Airplay is shown on the same panel.